The Inter Milan forward came off the bench to net the only goal five minutes from time to secure a 1-0 win over Slovenia in Florence.
The victory has left Italy unbeaten in Group C and eight points clear of nearest rivals Serbia in the battle to reach Poland and the Ukraine.
Italy have won seven of their last eight games and secured their place in next year's finals with two matches to spare.
"The credit belongs to the whole team, we believed, we looked for the goal until the end," Pazzini told www.figc.it.
The former Fiorentina player added: "It has been nice to have scored in Florence and most importantly an important goal like this."
Italy coach Cesare Prandelli saluted a "victory of courage".
He added: "We created several chances in the first half with a clear dominance in midfield.
"In this period it was difficult to find (a goal) because Slovenia defended very well.
"However, once the deadlock was broken, we played much better."